Reduced critical slowing down for statistical physics simulations

Abstract

Wang-Landau simulations offer the possibility to integrate explicitly over a collective coordinate and stochastically over the remainder of configuration space. We propose to choose the so-called "slow mode", which is responsible for large autocorrelation times and thus critical slowing down, for collective integration. We study this proposal for the Ising model and the linear-log-relaxation (LLR) method as simulation algorithm. We firstly demonstrate super critical slowing down in a phase with spontaneously broken symmetry and for the heatbath algorithms, for which autocorrelation times grow exponentially with system size. By contrast, using the magnetisation as collective coordinate, we present evidence that super critical slowing down is absent. We still observe a polynomial increase of the autocorrelation time with volume (critical slowing down), which is however reduced by orders of magnitude when compared to local update techniques.

arXiv commentAuthor accepted version for publication in Physical Review E, 15 pages, 15 figures

References in corpus (16)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Critical slowing down and error analysis in lattice QCD simulations
• The density of states method at non-zero chemical potential
• QCD at Fixed Topology
• The density of states in gauge theories
• The density of states approach to dense quantum systems
• Observation of FSS for a First Order Phase Transition
• Topological critical slowing down: variations on a toy model
• Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics
• Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model
• Anatomy of the sign-problem in heavy-dense QCD
• Topological susceptibility of pure gauge theory using Density of States
• Controlling the Sign Problem in Finite Density Quantum Field Theory
• The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation
• Free energy of the self-interacting relativistic lattice Bose gas at finite density

Cited by in corpus (2)

• Flow-based density of states for complex actions
• Advances in using density of states for large-N Yang--Mills